if he was to die without a will leaving her and a (dependent) child nothing, then she would have to make a claim against his estate under the inheritance and provision for dependents act 1975 within 3 months of probate (i think that deadline is right but check). she could still make a claim if had died with a will leaving her and a dependent daughter nothing under the same act claiming that they were both dependent (or just her if daughter is grown up as if not a dependent, then couldn't claim) and he should have made provision for them/her.
this would probably be very expensive for her and his estate and would provoke lots of bad feeling with the first family. she should sit him down and talk to him about both of them making a will and how he proposes to make sure that she and their daughter are taken care off so no feud erupts after death.